If ABC × DEED = ABCABC; where A, B, C, D and E are different digits, what are the values of D and E ?
- (a) D = 2, E = 0
- (b) D = 0, E = 1
- (c) D = 1, E = 0 ✓ UPSC's answer
- (d) D = 1, E = 2
Why the answer is (c)
• ABCABC is the three-digit number ABC written twice, which equals ABC × 1001 (for example, 123123 = 123 × 1001).
• So ABC × DEED = ABC × 1001, and DEED = 1001.
• Reading the digits, D = 1 and E = 0 — option (c).
• Hence option (c).
Why the other options are wrong
- (a) D = 2, E = 0
- D = 2, E = 0 gives DEED = 2002, which would double the number, not repeat it.
- (b) D = 0, E = 1
- D = 0, E = 1 gives 0110, not a four-digit number equal to 1001.
- (d) D = 1, E = 2
- D = 1, E = 2 gives 1221, not 1001.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.